There will be a bit of a fudge factor due to fingertips not being pointed in shape. I set the intonation by matching as best as possible/reasonable the 12th fret harmonic and the noted pitch when the string is pushed down. It is not hard to find the most "proper" place on the string for the harmonic, just listen for the clearest, loudest tone.

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If the neck is lined, use a small thin piece of metal like a paperclip to remove uncertainty about finger placement. Then, intonate as you would a fretted bass.
(I don't own a fretless, this is a best guess/suggestion)

Long-time FL player. In the lower positions, you can get away with centering the pad of your fingertip at the side dot (screw fingerboard lines because they generally force side dots into the realm of stupidity - off pitch; at "fretted locations" - great make me think 2x as much; how worthless is that?). But as you work your way up the neck, the ratio of your finger pad and the distance between proper pitch locations becomes very important.

You can get away with a half-assed intonation setup on FL if you have great ears and can wing it on the fly. Been there; done that. But your best bet is to match the open string with the octave harmonic.

There will be a bit of a fudge factor due to fingertips not being pointed in shape. I set the intonation by matching as best as possible/reasonable the 12th fret harmonic and the noted pitch when the string is pushed down. It is not hard to find the most "proper" place on the string for the harmonic, just listen for the clearest, loudest tone.

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Yep, this is what I've always done.

Looking at slareman's link to Gary Willis' instructions, notice that he highlited the word YOU. Set the intonations to be correct where YOU like to place your fingers. It's very personal, and as Jeff Scott says, there's a fudge factor involved.

I use a tuner and play the octave note accurately according to the fret markers and adjust intonation till my tuner displays an accurate pitch. After all it is a bit dependent on your technique as to where you place you LH finger. Thus my octave intonation is accurate with my LH technique!

I used to use the credit card, but found (I've been playing fretless since '88) that just putting my fingers on the string gets the intonation much more consistent with how I actually play. And, pfox14, that's WHY you set the intonation. Of course you have to make small adjustments, but setting the intonation makes where the stops are much more consistent along the whole neck and across all the strings. That in turn allows one to play more consistently and require less small adjustment.

On my lined fretless, I use a method á la Gary Willis (great link). For my unlined 5er I check 12th position dot indication vs harmonic on the lowest string but higher strings will be adjusted until it "feels correct", in lack of a better term. Of course the end result is quite similar either way.

All of you responders, thank you so much! You've all contributed helpful ideas. I appreciate it. While I'm realizing that I'm on the right track, I learned several things, plus the link to the Gary Willis tutorial was awesome. Thank you for that.

Being a former (and lately, possibly in present times, too) piano tuner, I'm pretty sensitive to the pitch, which is frustrating on one hand, but one the other hand, allows me to correct the pitch pretty quickly, an excercise that I've thoroughly enjoyed practicing. I just want to make sure all the reference possibilities were in place.

Thanx again. I've seen (and admittedly been part of) some topics that deteriorated into unfortunate snarkfests. All of you guys were great.

Finding the octave node will indicate where to place your finger on the what would be the 12th fret on a fretted instrument. When you finger the octave in that position, is the note sharp or flat? Sharp, saddle is too far forward, flat, too far back. Adjust until it is right. This is not exact as the slightest change in your hand posture will change the pitch but this will provide a way to intonate the instrument pretty closely and now you must use your ears.